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Im a bit confused about the solution to this,

It shows a graph, and then explains why the graph is not planar, by showing a $K_{3,3} minor $enter image description here

enter image description here

So can anyone help explain what is going on in this picture?

Thanks

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Each blue ellipse is a "left vertex" of $K_{3,3}$ and each green ellipse is a "right vertex" of the same graph. The edges covered by the ellipses are contracted to give the minor and the top vertex of the star is simply omitted.

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    And you can simply just delete any vertex when looking for a minor correct? – 2017-02-09
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    Yes, extracting a [graph minor](https://en.wikipedia.org/wiki/Graph_minor) involved deleting vertices and edges, and contracting some of the other edges. – 2017-02-09